A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning them properly may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize internal dynamics of a class of RNNs called echo state networks (ESNs). We design pr...

We introduce a statistical method to investigate the impact of dyadic relations on complex networks generated from repeated interactions. It is based on generalised hypergeometric ensembles, a class of statistical network ensembles developed recently. We represent different types of known relations between system elements by weighted graphs, separated in the different layers of a multiplex netw...

The analysis of temporal and spatial patterns of gene expression is critically important for many kinds of developmental studies, including the construction of gene regulatory networks. Recently, multiplex, fluorescent, whole mount in situ hybridization (multiplex F-WMISH), applied in combination with confocal microscopy, has emerged as the method of choice for high-resolution, three-dimensiona...

Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transit...

We present an analytical approach for bond percolation on multiplex networks and use it to determine the expected size of the giant connected component and the value of the critical bond occupation probability in these networks. We advocate the relevance of these tools to the modeling of multilayer robustness and contribute to the debate on whether any benefit is to be yielded from studying a f...

Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model random dot product graph. However, they not well developed more complex network structures, which becoming increasingly common in practice. In this article we propose a new latent multiplex networks, i.e., multiple heterogeneous observed ...

What do societies, the Internet, and the human brain have in common? The immediate answer might be " not that much " , but in reality they are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons. In the last two decades, network scientists have...

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Pe...

This paper presents a WDM (Wavelength Division Multiplex) mesh network planning and designing that satisfies given demands and a restoration approach. This restoration approach is based on the network traffic rearrangement by all source and destination nodes with the shortest path algorithm ignoring the failed link and when a link has inadequate capacity, the problem is solved by both nodes of ...

Network ecology is a rising field of quantitative biology representing ecosystems as complex networks. A suitable example is parasite spreading: several parasites may be transmitted among their hosts through different mechanisms, each one giving rise to a network of interactions. Modelling these networked, ecological interactions at the same time is still an open challenge. We present a novel s...